ABOUT GEOMETRY ON SUBSPACES IN

Botirjon Mamadaliev; Madinabonu Davlatboeva

Mathematics

No. 3 (2024): FarDU.Ilmiy xabarlar jurnali. Ilova to'plam (Aniq va tabiiy fanlar)

ABOUT GEOMETRY ON SUBSPACES IN

Mamadaliev Botirjon Mullaaminovich^▸^▾
Davlatboeva Madinabonu Ikromjonovna^▸^▾

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Submitted: August 13, 2024
Published: 2024-09-12

Abstract

The paper investigates geometry and its manifolds on subspaces, a five-dimensional pseudo-Euclidean space of index two. Geometry in the sphere of real radius is defined. The existence of all hyperbolic spaces of dimension three and some four-dimensional hyperbolic spaces is proved, as well as a manifold of maximum dimension.

References

Владимиров Ю.С., Геометрофизика. – М.: БИНОМ. Лаборотория знаний, 2006. – 600 стр.
. Розенфельд Б.А. Неевклидовы пространства. М.: Наука, 1969. - 548с.
. А.Артыкбаев., Соколов Д. Д. Геометрия в целом в плоском пространсве – времени, Ташкент: Фан, 1990., 180с.
. Artykbaev A., Sultanov B.M. Invariants of a second-order curves under a special linear transformation // Uzbek mathematical journal. №3. (2019), pp.19-26.
. Artykbayev A., Mamadaliyev B.M. Geometry of Two-Dimensional Surfaces in Space // Lobachevskii Journal of Mathematics, 2023. Volume 44, Issue 4. –P. 1243-1247. (3. Scopus Q2, Cite Score IF=0.42).
. Mamadaliyev B.M. Geometry of complete two-dimensional surfaces in a five-dimensional pseudo-euclidean space of index two // Bulletin of the Institute of Mathematics, 2023. Volume. 6, Issue 2, –P 31-43. (01.00.00. № 6).

[1] Владимиров Ю.С., Геометрофизика. – М.: БИНОМ. Лаборотория знаний, 2006. – 600 стр.

[2] . Розенфельд Б.А. Неевклидовы пространства. М.: Наука, 1969. - 548с.

[3] . А.Артыкбаев., Соколов Д. Д. Геометрия в целом в плоском пространсве – времени, Ташкент: Фан, 1990., 180с.

[4] . Artykbaev A., Sultanov B.M. Invariants of a second-order curves under a special linear transformation // Uzbek mathematical journal. №3. (2019), pp.19-26.

[5] . Artykbayev A., Mamadaliyev B.M. Geometry of Two-Dimensional Surfaces in Space // Lobachevskii Journal of Mathematics, 2023. Volume 44, Issue 4. –P. 1243-1247. (3. Scopus Q2, Cite Score IF=0.42).

[6] . Mamadaliyev B.M. Geometry of complete two-dimensional surfaces in a five-dimensional pseudo-euclidean space of index two // Bulletin of the Institute of Mathematics, 2023. Volume. 6, Issue 2, –P 31-43. (01.00.00. № 6).